Given:
Number of miles covered = [tex]2\dfrac{1}{2}[/tex]
Length of each lap = [tex]\dfrac{5}{6}[/tex] of a mile.
To find:
The number of laps.
Solution:
We know that,
[tex]\text{Number of laps}=\dfrac{\text{Number of miles covered}}{\text{Length of each lap}}[/tex]
[tex]\text{Number of laps}=\dfrac{2\dfrac{1}{2}}{\dfrac{5}{6}}[/tex]
[tex]\text{Number of laps}=\dfrac{\dfrac{5}{2}}{\dfrac{5}{6}}[/tex]
[tex]\text{Number of laps}=\dfrac{5}{2}\times \dfrac{6}{5}[/tex]
[tex]\text{Number of laps}=3[/tex]
Therefore, Grayson ran 3 laps.
Determine the equation of the line. (slope intercept form)
Answer:
y=x-4
Step-by-step explanation:
y=mx+b
m : slope : 1
b : y-int : -4
which expressions are equivalent to the one below? Check all that apply.
[tex]8^x[/tex]
A. x^4
B. 8 * 8^x+1
C. (32/4)^x
D. 8 * 8^x-1
E. 32^x/4^x
F. 32^x/4
AP_EX - Algebra II
Answer:
The right answers are C, D and E
AYO HELP ME OUT! PLEASE ONLY FULL ANSWERS <3
Answer:
x=32°
Step-by-step explanation:
ABC+BCA+CDE=180
Substitute
61+57+2x=180
118+2x=180
2x=62
x=32
54x x 654v = 43695v solve for v
a) 5√160=
b) √245=
c) 3√72=
d) √50=
e) √18=
e) 4√243=
f) 3√576 =
g) √300=
Answer:
a) 20[tex]\sqrt{35}[/tex]
b) 7[tex]\sqrt{5}[/tex]
c) 18[tex]\sqrt{2}[/tex]
d) 5[tex]\sqrt{2}[/tex]
e) 36[tex]\sqrt{3}[/tex]
f) 72
g) 10[tex]\sqrt{3}[/tex]
Step-by-step explanation:
For brainiest :):):):):):)):):):)
Answer:
9) 0.46
10) 0.666
11) 18%
12) 2.3%
13) 0.7/ 70%
14) 0.56/ 56%
15) 0.0035/ 0.35%
16) 1.13/113%
Step-by-step explanation:
Help and Plz make sure it’s right
Answer:
8.6
Step-by-step explanation:
Use the pythagorean therom for this
(5.9)^2 + (6.3)^2 = c
c= 74.5
square root of 74.5 is 8.631 or 8.6
hope this helps
You Try: Solve for x and y by using elimination. 4x + y = 7 4x - 2y = -2
Answer:
[tex]\boxed {\boxed {\sf (1, 3) \ or \ x=1 \ and \ y=3}}}[/tex]
Step-by-step explanation:
We are given this system of equations:
[tex]4x+y=7\\4x-2y=-2[/tex]
We use elimination to solve to eliminate one of the variables, so we only have to work with one at a time. We do this by adding and subtracting the equations, and sometimes multiplying the entire equation by a number.
Notice how both equations have a 4x. This means they can easily be eliminated, without multiplying the equations by another number first. Let's subtract the 2 equations.
[tex]\ \ \ 4x+y=7\\ -(4x-2y)=-2[/tex]
The 4x will cancel because 4x-4x=0.
[tex]\ \ \ \ y=7 \\ - (-2y) = -2[/tex]
Since there are back to back negative signs, they become addition signs.
[tex]\ \ \ \ y=7 \\+2y=2[/tex]
[tex]3y=9[/tex]
We are solving for y , so we must isolate the variable. It is being multiplied by 3 and the inverse of multiplication is division. Divide both sides by 3.
[tex]3y/3=9/3\\y=3[/tex]
Now we can substitute 3 in for y in the original equations. Let's use the first one.
[tex]4x+y=7\\4x+3=7[/tex]
3 is being added to 4x. The inverse of addition is subtraction. Subtract 3 from both sides.
[tex]4x+3-3=7-3\\4x=4\\[/tex]
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.
[tex]4x/4=4/4\\x=1[/tex]
x is equal to 1 and y is equal to 3. Coordinate points are written as (x, y). The solution to this system of equations is (1, 3).
A statue of George Washington is also in Druid Hill Park. If a girl stands 15 m away from the statue, and places a mirror 12 m from the statue (3 m from her feet), she can see the top of the statue in the mirror. The girl's height is 5.5 ft. How tall is the statue?
Answer:
The statue is 22ft tall.
Step-by-step explanation:
Here we will have two similar triangle rectangles.
One is made between the girl's feet, the mirror, and the girl's eyes.
So in this case the catheti are:
the distance between the girl and the mirror (3 m) and the height of the girl (5.5 ft)
The other triangle rectangle has the vertices:
The mirror, the base of the statue, and the top of the statue.
Such that the catheti of this triangle are the distance between the base of the statue and the mirror (12m) and the height of the statue (we want to know this, let's call this X for the moment).
Because the triangles are similar, this means that there is a proportionality constant between each correspondent side, let's call this k.
Then the distance between the girl and the mirror must be k times the distance between the base of the statue and the mirror:
3m = k*12m
And the height of the girl must be k times the height of the statue.
5.5ft = k*X
You can see that we have different units, this does not matter because k is a dimensionless constant.
With the first equation we can find the value of k
3m = k*12m
3m/12m = k
(3/12) = 1/4 = k
Now we can replace this in the other equation to get:
5.5ft = (1/4)*X
Solving this for X we get:
(5.5ft)*4 = X
22ft = X
The height of the statue is 22ft.
There are 90 students in the school band. 40% of them are sixth graders. How many band members are sixth graders?
Answer:
36
Step-by-step explanation:
.4 x 90
Answer:
36
Step-by-step explanation:
40/100 = x/90
100x div 100 3600div 100
x = 36
Work out the area of a rectangle with base,
b
= 26mm and perimeter,
P
= 70mm
BRAINLIEST!!!! PLZZZZ SEE BELOW!!!
Answer:
b. 0.25
Step-by-step explanation:
40 + 120 = 160
40 / 160
What is the volume of a sphere with a diameter of 4.9 cm, rounded to the nearest
tenth of a cubic centimeter?
Answer:
492.87cm^3
Step-by-step explanation:
Given data
Diameter= 4.9cm
The expression for the volume is
V= 4/3 πr^3
Substitute
V= 4/3*3.142*4.9^3
V= 4/3*3.142*117.649
V=1478.612632 /3
V=492.87 cm^3
Hence the volume is 492.87cm^3
Please help! Describe how the variables in the given equation are related.[tex]p=\frac{kqrt}{s}[/tex]
9514 1404 393
Answer:
p is proportional to q, r, t, and inversely proportional to s
Step-by-step explanation:
Assuming k is a "constant of proportionality," the value of p is directly proportional to each of the numerator variables: q, r, t. P is inversely proportional to the denominator variable, s.
Can someone help me plzzz and thank you
Answer:
Yes SAS
Step-by-step explanation:
2 sides are the same
1 90 degree angle for each triangle
Hence the Answer Side-Angle-Side
Ellane plan to interview some applications for positions in her office she scheduled a 1/4 of an hour to meet each of them how much time did she schedule for all six appliances
Answer:
1 1/2 hours
Step-by-step explanation:
To determine the time she would spend on 6 applicants, multiply the time she spends on each applicant by the total number of applicants
1/4 x 6 = 6/4 = 1 2/4 hours
to convert to its simplest form, divide both numerator and denominator by 2. this gives 1 1/2 hours
Another method
Add 1/4 six times
1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 6/4 = 1 2/4 = 1 1/2 hours
Manuel incorrectly claimed that the surface area of the cylinder
shown is about 621.7 in.. Use a formula to find the surface area of the cylinder.
Use 3.14 for it. What was his likely error?
11 in
The surface area of the cylinder is about
(Round to the nearest tenth as needed.)
Answer:
25.9%
Step-by-step explanation:
Since, the actual dimensions of the cylinder is not given we can assume the some dimension to explain the problem
Let us assume the dimension of the cylinder be
radius= 3in
height= 5 in
The expression for the total surface area of a cylinder is
T. S. A. =2πrh+2πr^2
Let us plug in the values to to find TSA
T. S. A. =2×3.14×3×5+2×3.14×3^2
Solving we get
T. S. A. =94.26+56.556
T. S. A. =150.816 in^2
Now let us find the error
we know that error % is calculated as
%error= [actual value-expected value/expected value]×100
%error= [190 -150.816/150.816]×100
%error= [39.184/150.816]×100
%error= 0.259×100
%error= 25.9%
Solve the question in the picture below. Thank you.
Answer:
8 units
Step-by-step explanation:
Find the distance along the y-axis. For the example points (3,2) and (7,8), in which (3,2) is Point 1 and (7,8) is Point 2: (y2 - y1) = 8 - 2 = 6. This means that there are six units of distance on the y-axis between these two points. Find the distance along the x-axis. Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.
Tell whether x and y show direct variation, inverse variation, or neither.
y-3 = 22
the variables show: (inverse variation, direct variation, or neither)
Answer:
thWhat is c hw wrin hd dont know if I know what x is to find the answer
PLEASE helppppp me
I’ll give brainlest or whatever it’s called btw
Answer:
30.5 i think
Step-by-step explanation:
plz let me know if wrong!
Answer:
Step-by-step explanation:
the angles are equivalent, so set them equal to each other
4x + 2 = 124
- 2 - 2
4x = 122
/ 4 / 4
x = 30.5
Solve For X
5X + 30 = 110
Answer:
Your answer would be:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]5x + 30 = 110[/tex]
[tex]5x + 30 - 30 = - 30[/tex]
[tex]5x = 80[/tex]
[tex]x = 16[/tex]
Hope this helped! UwU
Julius is at point A He moves 3 units to the left and 2 units down from his
location and picks up a baill What are the coordinates of the points from where
he picked up the ball?
Answer:
(8, 10)
Step-by-step explanation:
He is at (11, 12). He moves three to the left, so 11 - 3 = 8. He then moves two down. 12 - 2 = 10. Therefore, he is at point (8, 10).
In ΔDEF, the measure of ∠F=90°, FD = 3.3 feet, and DE = 3.9 feet. Find the measure of ∠D to the nearest degree
Answer:
the awnser is 30 degrees
Step-by-step explanation:
You have to look at your d ruler between different angles
What is the measure of angle C
Answer:
41
Step-by-step explanation:
In order to find the measure of angle C we must find the value of x
Remember the measures of the angles in a triangle add up to equal 180
that being said we use this equation to solve for x
180 = (sum of angles) 63 + 2x + 8 + x + 7
now we solve
step 1 combine like terms
63 + 7 + 8 = 78
2x + x = 3x
now we have 180 = 78 + 3x
step 2 subtract 78 from each side
180 - 78 = 102
78 - 78 cancels out
now we have 102 = 3x
step 3 divide each side by 3x
102/3=34
3x/3=x
we're left with x = 34
Now to find the measure of angle C
We plug in the value of x in the expression (x + 7)
so c = 34 + 7
34 + 7 = 41
therefore your answer is 41
N artist makes three types of ceramic statues (large, medium, and small) at a monthly cost of $760 for 210 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $26, $18, and $15, respectively, how many of each type should be made to produce $3,640 in monthly revenue?
Answer:
20, 90 and 100
Step-by-step explanation:
Total number of statues = 210
Assuming that a large statue = x, medium statue = y and a small statue = z
Then, x + y + z = 210........i
Also, we're told that the monthly cost is $760, so
5x + 4y + 3z = 760.........ii
Cost of selling is $3640, so then
26x + 18y + 15z = 3640.........iii
Solving i and ii simultaneously, we have
5x + 5y + 5z = 1050
5x + 4y + 3z = 760
Subtracting, we have
y + 2z = 290.........iv
Again, solving ii and iii simultaneously, we have
130x + 104y + 78z = 19760
130x + 90y + 75z = 18200
On subtracting, we have
14y + 3z = 1560.........v
And finally, solving iv and v simultaneously, we also have
14y + 28z = 4060
14y + 3z = 1560
On subtracting,
25z = 2500
z = 2500 / 25
z = 100
Substituting for z = 100 in iv, we have
y + 2(100) = 290
y + 200 = 290
y = 290 - 200
y = 90
Substituting for y = 90, and z = 100 in i
x + 90 + 100 = 210
x + 190 = 210
x = 210 - 190
x = 20
Therefore, large statues has to be 20, medium statues has to be 90, and small statues has to be 100
9 less than 4 times a number equals 15
Answer:
if you wanted it in equation form the it'll be : 9 < 4 x n = 15
~ i hope this has helped you out, have a gr8 day/night my friend!~
Step-by-step explanation:
Answer:
Six / 6
Step-by-step explanation:
Fifteen less than 4 times a number is 9, meaning we have to find the number.
Let the required number be x
4 times the number = 4x
15 less than 4 times the number = 4x-15
⇒ 4x – 15 = 9
⇒ 4x = 9 + 15
⇒ 4x = 24
⇒ x = 6
meaning the number is 6.
Hope this helps!
PLISSSSSSSSSSS HELPPPPPPP..............................
Answer:
it would be 9 cause with start counting the 7- to 2 its gonna be nine
Step-by-step explanation:
Which expression is equivalent to `7+10x+x-3?`
Are the two triangles congruent ? Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!
Answer:
No
Step-by-step explanation:
None of the angles in the two triangles match, so it is impossible for them to be congruent.
f(x) = 3 x e^2x
That's the problem
Answer:
6 e (*2)x
Step-by-step explanation:
i hope this helps and the 2 is a square unit
Answer:
y = 0
Step by step explanition:
